Notes. Gaseous disk It has a surface density Σ₀ and aspect ratio h₀ at a reference radius of r₀, and it extends from r_min to r_max. P and Q are the power-law indexes for the density and aspect-ratio profiles, respectively (Equations (10) and (11)). T_d is the dispersal timescale of the gas disk, and $T_d^{+}$ is the acting timescale for the outward migration defined as one-third of T_d. Planetesimal disk It is composed of N massless particles with each particle initialized with a semimajor axis a randomly such that they follow a power law ∝ a^–0.5 from a_min to a_max. The rest of the orbital elements, inclination (I), argument of periapsis (ω), longitude of the ascending node (Ω), and true anomaly (f) are randomly chosen. Planets The planets have initial and fixed mass m_p and initialized with a semimajor axis of a_init. The inward-migration timescale τ_α is defined for Planet b; meanwhile, the outward-migration timescale ${\tau }_a^{+}$ is defined for the rest. These outward-migrating planets have an upper limit for the semimajor axis a_lim and $\tilde{\Gamma }$ is the normalized torque.